Electron beams are increasingly coming into use in the radiation treatment of cancer because their rapid dose falloff minimizes irradiation of critical healthy tissues beyond the treatment volume. Unfortunately, for treatment planning purposed it is not yet possible to routinely calculate the absorbed dose distribution precisely, particularly in the presence of tissue inhomogeneities and body curvature. In penetrating the body, high-energy electrons suffer a great many collisions and follow a tortuous, although mainly forward, path. It has only been recently that a number of investigators have begun to apply Fermi-Eyges multiple scattering theory to the problem of electron dose calculation, recognizing that this theory describes the behavior of the electron beam as a reasonable first approximation, at least in a homogeneous or horizontally layered medium. However, the Fermi-Eyges theory cannot be applied directly to calculating electron dose distributions for configurations with localized inhomogeneities, and some sort of approximate pencil-beam summation method must be use for such configurations if the Fermi-Eyges theory is to be used. The goal of this ongoing research project is to develop an electron dose calculation algorithm which is sufficiently accurate in the most complicated situations expected to be encountered clinically, yet practical in the sense of being able to be implemented in a computerized treatment planning system (short enough calculation time). Producing such an algorithm entails starting with our general Gaussian multiple-scattering theory and developing from it appropriate theory which is more accurate than the Fermi-Eyges theory, and which provides the immediate calculation of dose directly from (three-dimensional) CT scan data, even for arbitrary configurations of localized inhomogeneities. Besides the multiple scattering process, various secondary effects are to be incorporated into the computational algorithm. Extensive Monte Carlo computer work is envisioned in the development and verification of the algorithm.